Suppose I have a word like
English Language Learners Stack Exchange is a question and answer site for speakers of other languages learning English. It only takes a minute to sign up.Sign up to join this community
At the beginning of a sentence, first letter only, unless if the thing's actual name has either both words or the second word with initial caps.
e.g. e-mail -> E-mail, but Wite-Out is Wite-Out and pro-Randy -> Pro-Randy
Otherwise, it's typically the generic parts (i.e. not proper nouns) of the word that are not capitalized, while proper nouns in the hyphenated structure are.
e.g. pro-choice, anti-socialist, no-brainer, meat-eating;
Mario-loving, anti-Luigi, pro-Republican